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We study the effects that ripples induce on the electrical and magnetic properties of graphene. The variation of the interatomic distance created by the ripples translates in a modulation of the hopping parameter between carbon atoms. A tight binding Hamiltonian including a Hubbard interaction term is solved self consistently for ripples with different amplitudes and periods. We find that, for values of the Hubbard interaction $U$ above a critical value $U_C$, the system displays a superposition of local ferromagnetic and antiferromagnetic ordered states. Nonetheless the global ferromagnetic order parameter is zero. The $U_C$ depends only on the product of the period and hopping amplitude modulation. When the Hubbard interaction is close to the critical value of the antiferromagnetic transition in pristine graphene, the antiferromagnetic order parameter becomes much larger than the ferromagnetic one, being the ground state similar to that of flat graphene.
One of the most exciting phenomena observed in crystalline disordered membranes, including a suspended graphene, is rippling, i.e. a formation of static flexural deformations. Despite an active research, it still remains unclear whether the rippled p
In recent experiments, time-dependent periodic fields are used to create exotic topological phases of matter with potential applications ranging from quantum transport to quantum computing. These nonequilibrium states, at high driving frequencies, ex
Graphene epitaxially grown on Ru(0001) displays a remarkably ordered pattern of hills and valleys in Scanning Tunneling Microscopy (STM) images. To which extent the observed ripples are structural or electronic in origin have been much disputed recen
The exceptionally high mobility of carriers in graphene is one of its defining characteristics, especially in view of potential applications. Therefore it is of both practical and fundamental importance to understand the mechanisms responsible for li
We report measurements of the effects of a random vector potential generated by applying an in-plane magnetic field to a graphene flake. Magnetic flux through the ripples cause orbital effects: phase-coherent weak localization is suppressed, while qu